QJEEM19Mae3bb: JEE Main 2019 Mathematics - Class 11 JEEM19Mae3bb Solution: A point P moves on the line 2x – 3y + 4 = 0. If Q(1, 4) and R…

Question

Verified Solution • 2025–26 Session moderate

A point P moves on the line 2x – 3y + 4 = 0. If Q(1, 4) and R (3, – 2) are fixed points, then the locus of the centroid of

Δ

PQR is a line :

Accepted Answer

Let the centroid of

Δ

PQR is (h, k) & P is (

α

,

β

), then

\frac{α + 1 + 3}{3} = h

and

\frac{β + 4 - 2}{3} = k

α = (3 h - 4)

β = (3 k - 4)

Point P(

α

,

β

) lies on the line 2x

-

3y + 4 = 0

∴

2(3h

-

4)

-

3 (3k

-

2) + 4 = 0

\Rightarrow

locus is 6x

-

9y + 2 = 0

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